Israel Journal of Mathematics

, Volume 223, Issue 1, pp 205–259 | Cite as

The Hölder property for the spectrum of translation flows in genus two

  • Alexander I. Bufetov
  • Boris Solomyak


The paper is devoted to generic translation flows corresponding to Abelian differentials with one zero of order two on flat surfaces of genus two. These flows are weakly mixing by the Avila–Forni theorem. Our main result gives first quantitative estimates on their spectrum, establishing the Hölder property for the spectral measures of Lipschitz functions. The proof proceeds via uniform estimates of twisted Birkhoff integrals in the symbolic framework of random Markov compacta and arguments of Diophantine nature in the spirit of Salem, Erdős and Kahane.


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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Aix-Marseille UniversitéCNRS, Centrale Marseille, I2M, UMR 7373MarseilleFrance
  2. 2.Steklov Mathematical Institute of RASMoscowRussia
  3. 3.Institute for Information Transmission ProblemsMoscowRussia
  4. 4.National Research University Higher School of EconomicsMoscowRussia
  5. 5.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael

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